This is a simple question, but I just don't understand how we determine the poles and zeros of a rational system function.
For example, for the LTI system described by this constant coefficient difference equation $$ y[n]-\frac{5}{2}y[n-1]+y[n-2]=x[n] $$ we can determine that
$$ H(z)=\frac{1}{(1-\frac{1}{2}z^{-1})(1-2z^{-1})} $$
I understand why there are poles at $z=\frac{1}{2}$ and $z=2$, but I don't understand why there are two zeros at $z=0$. Even if I multiply $H(z)$ through by $z$, there would only be one zero, correct?